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Identifier 000453647
Title Non-hermitian phenomena in photonic systems
Alternative Title Μη ερμιτιανά φαινόμενα σε φωτονικά συστήματα
Author Κόμης, Ιωάννης Γ
Thesis advisor Μακρής, Κωνσταντίνος
Reviewer Τσιρώνης, Γεώργιος
Κομίνης, Ιωάννης
Ζώτος, Ξενοφών
Σωτηριάδης, Σπυρίδων
Παπάζογλου, Δημήτρης
Καφεσάκη, Μαρία
Abstract From its very beginning Quantum Mechanics theory was based on axioms. One of them states that every physical observable is associated with a Hermitian operator ensuring the reality of the energy spectrum and a complete set of eigenfunctions. By the end of the nineties however, Carl M. Bender and Stefan Boettcher proved that this constrain can be relaxed. Non-Hermitian Hamiltonians might have real spectrum if and only if they commute with the combined action of Parity P and Time T operators. Since their first introduction and realization in the field of optical physics by Prof. Christodoulides and his group, this new regime of P T -symmetric Hamiltonians brought a plethora of intriguing phenomena in physics. In particular, coupled waveguides or microcavities that combine gain and loss in a particular way can realize P T - symmetric optical potentials. Such complex systems have novel functionalities and various applications in laser physics, sensing, imaging and integrated photonics. The framework of this thesis is that of optics and non-Hermitian physics in photonic guided structures. We focus on the underlying physics of such novel systems and discuss their potential applications. In the fourth chapter, a novel type of waves is examined in the context of non- Hermitian photonics. We can identify a class of complex guided structures that support localized paraxial solutions whose intensity distribution is exactly the same as the intensity of a corresponding solution in homogeneous media (free or bulk space). In other words, intensity-wise the two solutions are identical and their phase is different by a factor exp[iθ(x,y)]. The non-Hermitian potential is determined by the phase θ, as well as the amplitude and phase of the bulk space solution that contributes to the imaginary and real part of the potential, respectively. That way we can connect the plane waves and Gaussian beams of free space to constant-intensity waves and what we call the equal-intensity waves (EI waves) in non-Hermitian media. Such a relation allows us to study three different physical problems: Propagating EI waves inside random media, interface lattice solitons, and moving solitons in photonic waveguide structures with free-space characteristics. The relation of EI waves to unidirectional invisibility and Bohmian photonics is also examined. These types of waves were recently observed by A. Steinfurth, I. Kreši´c, S. Weidemann, M. Kremer, K. G. Makris, M. Heinrich, S. Rotter, and A. Szameit, Science Advances 8, 21 (2022). In the fifth chapter, we focus more on non-Hermitian photonics of waveguide systems. Topology, parity-time symmetry, and nonlinearity are at the origin of many fundamental phenomena in complex systems across the natural sciences, but their mutual interplay remains unexplored. In particular,non-Hermitian topological systems simultaneously posses two antagonistic features: ultra sensitivity due to exceptional points and robustness of topological zero energy modes, and it is unclear which one prevails under different perturbations. We study that question by applying the pseudospectra theory on the prototypical non-Hermitian Su-Schrieffer-Heeger (NHSSH) lattice. Topological modes around the underlying third order exceptional point (EP3) are robust with respect to chiral perturbations but sensitive to diagonal perturbations. In fact, exactly at the EP3 the chiral symmetry leads to a suppressed sensitivity, that corresponding to thatmanifested at an EP2. Finally, for nonlinearly induced perturbationswe provide a connection between the pseudospectrumapproach and a nonlinear phase shift, which is relevant for experiments. Our work led to a recent publication in Science (2021) journal, with experimental and theoretical results. Solitons lie in the heart of nonlinear optics and thus, are relevant to the content of our thesis. In the seventh chapter we introduce a novel type of lattice solitons the so called skin solitons in Hatano-Nelson systems. In the next chapter, we also examine the angular sensitivity of lattices close to the exceptional point and under a wide beam excitation. More specifically, we identify the conditions under which the exceptional point of an optical lattice can be excited. We connect our dynamical analysis to the spectral sensitivity of the problem in terms of pseudospectra. Finally, we present theoretical results on a inverse design method (based on su-peroscillations) that allow us to construct an optical mask for subwavelength focusing using solutions of the paraxial equation of diffraction in bulk. Our approach is based on superpositions of Laguerre-Gaussian (LG) beams, by imposing subwavelength features.
Language English
Subject Exceptional points
Guided structures
Non-hermitian photonics
Nonlinear optics
Optics
Parity-time symmetry
Star formation
Topological physics
Ιδιάζοντα σημεία
Καθοδηγούμενες δομές
Μη γραμμική οπτική
Μη ερμιτιανή φωτονική
Οπτική
Τοπολογική φυσική
Χωροχρονική συμμετρία
Issue date 2023-02-13
Collection   School/Department--School of Sciences and Engineering--Department of Physics--Doctoral theses
  Type of Work--Doctoral theses
Permanent Link https://elocus.lib.uoc.gr//dlib/6/c/f/metadata-dlib-1675162279-991678-31402.tkl Bookmark and Share
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